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proteinsSTRUCTURE O FUNCTION O BIOINFORMATICS
HingeMaster: Normal mode hingeprediction approach and integrationof complementary predictorsSamuel C. Flores,1,2* Kevin S. Keating,3 Jay Painter,4 Faruck Morcos,5 Khang Nguyen,2
Ethan A. Merritt,4 Leslie A. Kuhn,6,7,8 and Mark B. Gerstein2,3,9*1Department of Physics, Yale University, Bass 432, New Haven, Connecticut 06520
2Department of Molecular Biophysics and Biochemistry, Yale University, Bass 432, New Haven, Connecticut 06520
3 Program in Computational Biology and Bioinformatics, Yale University, Bass 432, New Haven, Connecticut 06520
4Department of Biochemistry, University of Washington, Mailstop 357742, Seattle, Washington 98195-7742
5Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, Indiana 46556
6Department of Biochemistry & Molecular Biology, Michigan State University, East Lansing, Michigan 48824
7Department of Computer Science & Engineering, Michigan State University, East Lansing, Michigan 48824
8Department of Physics & Astronomy, Michigan State University, East Lansing, Michigan 48824
9Department of Computer Science, Yale University, Bass 432, New Haven, Connecticut 06520
INTRODUCTION
The structural information provided by the atomic coordinates of a
protein tells only part of the story of protein function. Much of the
remainder is told by the trajectory of motion. Motions can be classi-
fied according to the size of the mobile units, which may be frag-
ments, domains, or subunits, and according to packing as hinge, shear,
or other. Hinge bending motions are the largest single class of motions,
comprising 45% of the motions in a representative set.1,2 This class is
further subdivided into domain hinge motions (31% of the total)1 and
fragment hinge motions (13%). A logical first step towards the goal of
motion prediction for the case of domain hinge bending motions is to
predict the hinge location. In this work, we compare several existing
algorithms, present new ones, and combine all of these into HingeMas-
ter, a composite predictor.
The problem of hinge detection is easiest when two or more sets of
atomic coordinates are available for a given protein in different con-
formations. In that case, it is possible to visually inspect the pairs of
structures (as we have done in this work) and manually annotate the
hinge location. It is also possible to automate this using FlexProt or
(to some extent) other algorithms.3 Hinge detection based on two
structures is thus largely a solved problem. A much more challenging
problem arises when only one structure is known. In early work on
this problem, Janin and Wodak4 developed a domain interface area
Additional Supporting Information may be found in the online version of this article.
Grant sponsor: National Institutes of Health (NIH); Grant sponsor: Simbios, the NIH Roadmap for
Medical Research; Grant number: U54 GM072970; Grant sponsor: National Library of Medicine;
Grant number: T15 LM07056.
*Correspondence to: Samuel C. Flores, 266 Whitney Ave., New Haven, CT 06520. E-mail:
[email protected]; or Mark B. Gerstein, Yale University, Bass 432, New Haven, CT 06520.
E-mail: [email protected]
Received 1 June 2007; Revised 27 December 2007; Accepted 21 February 2008
Published online 23 April 2008 in Wiley InterScience (www.interscience.wiley.com).
DOI: 10.1002/prot.22060
ABSTRACT
Protein motion is often the link between struc-
ture and function and a substantial fraction of
proteins move through a domain hinge bending
mechanism. Predicting the location of the hinge
from a single structure is thus a logical first
step towards predicting motion. Here, we
describe ways to predict the hinge location by
grouping residues with correlated normal-mode
motions. We benchmarked our normal-mode
based predictor against a gold standard set of
carefully annotated hinge locations taken from
the Database of Macromolecular Motions. We
then compared it with three existing structure-
based hinge predictors (TLSMD, StoneHinge,
and FlexOracle), plus HingeSeq, a sequence-
based hinge predictor. Each of these methods
predicts hinges using very different sources of
information—normal modes, experimental ther-
mal factors, bond constraint networks, ener-
getics, and sequence, respectively. Thus it is logi-
cal that using these algorithms together would
improve predictions. We integrated all the meth-
ods into a combined predictor using a weighted
voting scheme. Finally, we encapsulated all our
results in a web tool which can be used to run
all the predictors on submitted proteins and vis-
ualize the results.
Proteins 2008; 73:299–319.VVC 2008 Wiley-Liss, Inc.
Key words: protein; motion; domain; hinge;
bending; atlas; flexibility; conformation; change;
molmovdb.
VVC 2008 WILEY-LISS, INC. PROTEINS 299
calculation method. The more recent FIRST algorithm5–9
identifies rigid substructures based on graph theoretic
calculations. FRODA uses these rigid units to simplify the
process of generating alternate structures which have been
shown to be consistent with NMR data for certain pro-
teins.10,11 The Gaussian Network Model (GNM)12 is an
approximate method for obtaining normal mode displace-
ments and consequent motional correlations of backbone
a-carbon atoms. Kundu et al. used the sign of the GNM first
normal mode displacement, with some postprocessing, to
assign residues to structural domains.13
A yet more challenging problem arises when only
sequence features (but no structural coordinates) are
known. In this article, we evaluate one predictor that
uses only sequence information. Relatively little work has
been reported on this largely unsolved problem,14,15 but
it is in some ways related to the more extensively studied
problem of detection of evolutionary domain boundaries
(which may or may not be flexible).15–18
In this work, we first introduce hNM, a family of
mostly novel hinge predictors based on normal modes.
The first member of this family, which we call hNMa for
simplicity, posits that the minima of the normalized
squared normal mode fluctuations should coincide with
hinges. This in itself is not novel but we show that for
the case of domain hinge bending, the first (rather than
any higher) normal mode is most informative, addressing
a point of some debate in the literature. A second, novel,
method designated hNMb detects the most rigid, contin-
uous structural domain through segmentation of normal
mode motional correlation matrices. Subsidiary predic-
tors hNMc and hNMd use similar information to find
additional hinges. To benchmark the method and com-
pare and integrate it with others, we use the Hinge Atlas
Gold (HAG), a set of proteins with carefully annotated
hinge locations.
We then turn our attention to existing methods, for
purposes of comparison and integration. We review the
following hinge predictors:
1. StoneHinge (Keating, et al. StoneHinge: A Hinge Pre-
diction Algorithm Using Rigidity Theory. Manuscript
in preparation, 2006) recognizes hinges as flexible
regions of the protein main chain intervening between
the two largest rigid domains (of at least 20 residues
each), as defined by ProFlex constraint-counting anal-
ysis of the protein’s covalent and noncovalent bond
network. Importantly, StoneHinge has some ability to
detect proteins that do not move by hinge bending,
but rather fall into some other classification.1 In the
latter case, hinge prediction results from other predic-
tors are likely to be inapplicable.
2. Translation Libration Screw Motion Determination
(TLSMD)19 divides the protein into segments whose
rigid body motions best account for the observed
distribution of temperature factors in a crystal structure.
3. The FO (FlexOracle20) family of hinge predictors gen-
erates protein fragments based on all possible loca-
tions of one or two cuts on the backbone. It is based
on the idea that structural domains fold independ-
ently, therefore when the cuts coincide with the hinge
location, the free energy of folding will be minimal
for the corresponding fragment pair.
4. HingeSeq15 is a hinge predictor based not on structure
but rather on sequence features.
These methods are complementary to each other and
to hNM family since they use very different information,
namely bond network topology, experimental thermal
factors, estimated domain free energy of folding, and
sequence. We run all of the predictors against the HAG,
then use various qualitative and quantitative measures to
benchmark and compare the performance of each
method. Lastly, we combine all of the methods using a
voting scheme to create a new predictor called Hinge-
Master.
THE hNM FAMILY OFNORMAL MODE BASEDHINGE PREDICTORS
hNMa: Which normal mode eigenvectoris most important for hinge prediction?
We begin our development with the hNM family of
hinge predictors. The name suggests its relationship to
HingeMaster (the integrated hinge predictor) and its reli-
ance on Normal Mode information. As mentioned, this
family has five members, designated hNMa to hNMe, of
which hNMb through hNMe are novel. The output of
hNMa is simply the normalized squared fluctuations due
to the first normal mode, with the idea that the minima
of this quantity coincide with the hinge location. This in
itself is not novel21 but the choice of first versus second
or higher modes is the subject of much debate in the
community,13,21,22 and it is this debate which we
address first.
Normal mode expansions provide the form of dis-
placements of a structure at each of a progressive series
of resonant frequencies, or excitation frequencies to
which an elastic structure responds strongly. Various
studies underscore the importance of low-order modes in
describing protein motion, but opinions vary as to which
of these should be used for hinge prediction. Alexandrov
et al.23 and Krebs et al.24 compared the successive nor-
mal modes of proteins with the displacements observed
from interpolated (‘‘morphed’’) structural pairs of pro-
teins, and found that the correlation was highest for the
lowest order mode, and decreased progressively for
higher modes. Kundu et al.13 assigned residues of pro-
tein to one of two clusters depending on the sign of the
S.C. Flores et al.
300 PROTEINS
lowest-order nontrivial normal mode eigenvector. These
domain assignments are then adjusted by a series of
physicochemically motivated postprocessing steps. Yang
and Bahar showed that catalytic sites tend to coincide
with regions of minimal displacement of the first and
second nontrivial mode.21 Here, we show that for the
case of domain hinge bending, the lowest-order nontri-
vial mode should be used for hinge prediction.
To do so, we will make use of the concept of a nodal
surface. To introduce this consider the example of a one
dimensional guitar string driven at its second harmonic
frequency. The string will have a nodal point in the mid-
dle which remains stationary. A drum head (effectively
two dimensional) similarly will have nodal lines, depend-
ing on which mode is excited. A three dimensional object
such as a tuning fork or a protein will have a surface
which describes the locus of points that remain station-
ary when the object vibrates at one of its normal fre-
quencies. The displacements of points on opposite sides
of this nodal surface have opposite sign.13 This surface is
in some sense a hinge, about which the motion occurs.
One might come away from prior work,12,23,25,26
with the following two ideas:
1. The nodal surface of the lowest order normal mode
eigenvector should coincide with the hinge location.
2. The nodal surfaces of the second, third, and higher
normal mode eigenvectors should also coincide with
the hinge, but to a lesser degree.
To test these, we extracted the mobility score, Mik for
each residue i in the kth mode, for k 5 1–7.21 This
quantity is the square fluctuation of residue i in mode k,
normalized such that the most mobile residue has mobil-
ity Mik 5 1 for mode k. We then generated one ROC
curve for each mode k. This is based on taking all resi-
dues with normal mode displacement lower than a cer-
tain threshold to be test positives and all others to be test
negatives. The ROC curves are generated by moving the
threshold and calculating sensitivity and specificity for
each possible threshold. We found that the first idea
above was correct; regions of low first normal mode dis-
placement are likely to coincide with hinge location (see
Fig. 1). The second and third normal mode displace-
ments were not correlated with hinge location, as
reflected by areas under the curve near 0.5. Modes higher
than three were also found to have very little correlation
with hinges (data not shown). Therefore the second idea
is incorrect. From this we concluded that if normal
mode displacements alone are used for hinge prediction
then it is the first rather than higher modes that alone
should be used. This is not to say that the higher modes
are useless; in the next section we will show that the cor-
relation matrix is generated by summing the correlations
due to all modes, and this matrix can be used effectively
for hinge prediction.
Motion correlation based methods(hNMb, hNMc, hNMd)
We now move on to describe applications of normal
modes to hinge finding. To do this we must first calcu-
late the normal mode motional correlations between a-carbon atoms in a protein. This is obtained by comput-
ing an expectation value in the Boltzmann ensemble. The
result is12,27:
g
3kBTDRi � DRj
� � ¼ ðC�1Þij
¼XN�1
k¼1
x�1k uk½ �i uk½ �j ¼ UX�1UT ð1Þ
Where G is the Kirchoff, or connectivity matrix, and X is
the diagonal matrix of eigenvalues xk of G. The elements
of G are simple to obtain approximately using the GNM
method.12 [uk]i is the displacement of the a-carbon of
residue i due to normal mode k. DRi is the net displacement
of the a-carbon of residue i from its equilibrium position
due to normal mode motions. g is the effective stiffness
used by Tirion et al.28,29 Cross-correlations are normalized
with respect to the auto-correlations as follows12:
Figure 1Lower values of the first normal mode displacement (solid line) correspond to
hinges, as shown by an area under the curve significantly greater than 0.5. The
same is not true of the second (dashed line) and third (dotted line) normal
modes, which have almost no predictive power. The slope at the origin is not
very steep, reflecting the fact that wide regions of proteins often had small or
zero displacement, leading to ambiguous predictions. Regions of high
displacement, however, were rather confidently excluded from containing hinges.
HingeMaster
PROTEINS 301
Cði; jÞ ¼ DRi � DRj
� �
DRi � DRih i DRi � DRih i½ �1=2ð2Þ
It is possible to inspect or analyze the cross-correlation
matrix C(i,j) by various methods30 and determine the
boundaries of domains. Figure 2(a) illustrates this—the
continuous domain is easily identified visually in this
case. The idea is that the motion of all the residues in a
domain should on average be correlated with that of all
other residues in the same domain. We therefore seek
submatrices of C(I,j) with high average values. Further,
these submatrices should be maximal in size so as to
favor finding the largest domains.
As a first step we compute the Average Correlation ma-
trix as follows:
A ðk; lÞ ¼1
ðl�kÞ2P
k< i�l; k<j�l
Cði; jÞ if k < l
0 if k ¼ l
Aðl; kÞ if k > l
8><>:
9>=>;
ð3Þ
As mentioned we seek large domains. To this end, we
therefore generate a matrix W(k,l) by weighting A(k,l) to
favor pairs k,l that are maximally distant from each other,
and are likely the endpoints of a structural domain:
W ðk; lÞ ¼ � l � kj j � Aðk; lÞ: ð4Þ
Lastly, we treat W(k,l) as a two-dimensional discrete
function of k,l and identify its minima using the algo-
rithm described for FlexOracle.20 The W(k,l) matrix,
again for Glutamine Binding Protein, with its global
minimum highlighted, is shown in Figure 2(b). hNMb
(Continuous Domain Boundary Identifier), hNMc and
hNMd (Excluded Region Identifier) all use this list of
minima, but treat it differently. hNMb ranks the minima
by the value of W(k,l) at the minimum. The particular
values of the indices k,l, where k < l at the location of the
global minimum are taken as the residue numbers of a
pair of hinge points. If k(l) is within five residues of the
N(C) terminus, then k(l) is dropped and the other index
is reported as the sole hinge point. The last modification
is that for the hinge point at k(l) the hinge is reported as
consisting of the two residues k 2 1 and k(l 2 1 and l).
hNMc goes through the same procedure, except it
ignores the lowest minimum (already reported by
hNMb) and processes all remaining minima as above. If
any hinge point is within five residues of a hinge point
corresponding to a lower minimum, the hinge point cor-
responding to the higher minimum is discarded.
hNMd (Excluded Region Identifier) works somewhat
differently. It is based on the idea that we may not be
able to precisely identify the flexible regions of protein,
but we can perhaps still identify parts of the protein
which are rigid, and surmise that the hinge may lie any-
where except in these rigid regions. For a minimum of W
located at residues k,l, it considers residues k 1 1 to l 2 2
to be part of a structural domain and excludes them
from consideration as a hinge. The process is repeated
with the remaining minima k,l of W (k,l). Any residues
that were not excluded after all minima have been con-
sidered in this way are reported as potential hinges.
Lastly, hNMe (Holm and Sander-like hinge predictor)
partitions the matrix differently from NMB with similar
goals. The correlation matrix [Eq. (2)] is partitioned by
separating the residues into two domains much as Holm
and Sander30 did for the contact matrix. A minor adjust-
ment is needed which is explained in the Supplementary
Methods section. This results in a reasonably good pre-
dictor (Table I) which has the added benefit of assigning
each residue to one of two domains, and also has no
intrinsic limitation with respect to number of hinge
points. We did not use this method in the current work,
however, since we found that the Continuous Domain
Boundary Identifier (hNMb) described above yielded bet-
ter results when measured by the associated P-values.
INTEGRATION OF HINGEMASTER
Gold standard
As we mentioned, in order to benchmark (and later
combine) hNM and the other prediction algorithms we
need a gold standard. In prior work, we found that hinge
annotations reported in the literature are obtained by a
wide variety of means, including NMR, proteolysis, sec-
ondary structure annotation, and normal modes.20
Rather than attempt to treat such disparate annotations
on an equal footing, in that work we compiled a set of
proteins which had all been crystallized in two different
conformations and exhibited hinge bending motion. This
provides direct evidence of the structural conservation of
domains through the course of motion. The hinges were
then identified based on determining which residue back-
bone degrees of freedom needed to be free such that the
observed conformational change could take place without
large steric clashes.15
Many of the HAG proteins were collected from the
Hinge Atlas, while others, such as Adenylate Kinase, Bio-
tin Carboxylase, Lactoferrin, and Calmodulin, are classic
hinge bending proteins widely used as test cases in the
community and were added where absent to make the
dataset represent proteins of broad interest as much as
possible. The use of protein motions studied by third
parties confirms that the annotated hinge points reflect
biologically or at least thermodynamically relevant
dynamics. We delve into this in greater depth for two
proteins in this paper, and several more in the supple-
mentary discussion. We will show that in some cases, we
S.C. Flores et al.
302 PROTEINS
Figure 2Glutamine Binding Protein (open), Morph ID: f205132-23662 PDB ID: 1GGG, HAG hinges (residues 85–86,176–177). Above, (A) and (B) illustrate the procedure for
generating hNMb and hNMd predictions. First, the a-carbon correlation matrix (plotted in a.) is obtained using GNM. In this case, residues ranging from 85 to 180 have
highly correlated motion (dashed turquoise box). To a somewhat lesser degree, residues 1–80 are also correlated (dotted turquoise box). A second matrix is obtained the
elements i,j of which contain the average correlation for a submatrix of the correlation matrix spanning residues i to j. This is then weighted by multiplying each element
by 2|i 2 j|. The resulting matrix is plotted in (b). The minima of this matrix correspond to the boundaries of structural domains which are continuous in sequence. The
most significant of these (in absolute value) is i,j 5 84,180, or equivalently 180,84 (dashed turquoise circles). A secondary minimum also exists at i,j 5 1,80. hNMb
therefore reports residues 84,85,180,181 as the predicted hinge location. hNMd works by excluding residues in continuous domains and reporting the remaining ones as
possible hinges. Therefore, hNMd reports residues 85–88 and 181–217 as hinges. In (C) we show the two-cut FlexOracle (FoldX) plot. The minimum at 83,179 is visible
(dashed turquoise circles). In (D) we show the protein colored by HingeMaster score. In (E) we show the output of the FO1, hNMa, HingeSeq, and HingeMaster
predictors (dotted black, dotted magenta, dash-dotted cyan, and solid red traces, respectively) and the HAG hinge locations (green X’s).
HingeMaster
PROTEINS 303
predict a hinge where none is annotated in the HAG, but
for which some evidence exists in the literature. In these
cases that HAG annotation was not modified, since the
point of the HAG is to be objective rather than compre-
hensive. These cases demonstrate that the predictors can
detect previously unknown motion.
StoneHinge
We earlier introduced the novel hNM family of predic-
tors, and now move on to describe the existing predic-
tors. The first of these is StoneHinge, which predicts
hinges using the FIRST algorithm6 as implemented in
the freely available ProFlex software. ProFlex is designed
to analyze flexibility in proteins and uses a 3D constraint
counting algorithm based on rigidity and graph theory.
This approach ultimately derives from the structural en-
gineering work of James Clerk Maxwell,31 designed to
assess whether the trusswork of a bridge would be
adequate to ensure stability. The same concepts have
been shown to be mathematically robust for analyzing
the 3-dimensional covalent and noncovalent bond net-
works in proteins.32 The FIRST algorithm6,33 thus
counts local degrees of bond-rotational freedom. This
divides the protein into two types of regions: those that
are constrained and therefore rigid, and those that are
underconstrained and therefore free to rotate. A rigid
region consists of a group of atoms that do not move rel-
ative to each other due to the constraints of the bond
network. However, two rigid regions may move relative
to each other, like two stones connected by a flexible
tether.
A key part of this analysis involves representing the
essential noncovalent interactions (hydrogen bonds, salt
bridges, and hydrophobic interactions) that cross-
bridge the protein structure.8 These interactions vary
in energy and can be separated by invoking an energy
threshold. All interactions that are lower in energy
(more favorable) than this threshold are included in
the analysis, while those that are higher in energy (less
favorable) than the threshold are ignored. To obtain
flexibility analysis results reflecting ‘‘native-like’’
motion, this threshold is varied from protein to pro-
tein. We describe the process of selecting the correct
threshold below.
StoneHinge builds on the FIRST algorithm and uses
it to predict hinge motion. FIRST iteratively varies the
threshold and examines the resulting bond-constraint
network to find the boundaries of the rigid regions.
The size, location, and number of the rigid regions will
vary according to the threshold. StoneHinge selects the
value of the threshold that results in a second-largest
rigid region of maximal size. It then finds the flexible
region or regions connecting the two largest rigid
regions. These flexible regions are then reported as
hinges.
StoneHinge typically requires that both rigid domains
contain at least 20 residues. If two rigid domains of this
size can not be found, then StoneHinge reports that any
detected flexible residues are unlikely to contribute to a
hinge bending motion, as domains of this size typically
result from flexible loops or similarly small motions.
However, this restriction was ignored for purposes of
generating HingeMaster predictions.
Before the above analysis is carried out, StoneHinge
performs some preprocessing steps as follows. It first
removes all heteroatoms from the Protein Data Bank for-
matted structure files. These include inhibitors, ligands,
and cofactors, as they may stabilize the protein in the
ligand-bound conformation and cause the hinge region
to no longer appear flexible. Additionally, it adds hydro-
gen atoms to the structure using GROMACS,34,35 as
they are required to calculate hydrogen bond energies,
which are dependent on angular geometry as well as dis-
tance. Lastly, it removes all water molecules from input
crystal structures. While ProFlex works best with only in-
ternal water molecules included, which can potentially be
important for stabilizing protein structure, the effects of
these waters are typically minimal.36 As little difference
was found in the hinge predictions when using vs. omit-
ting entrained water molecules, (Keating, K., et al.,
StoneHinge: A Hinge Prediction Algorithm Using Rigid-
ity Theory. Manuscript in preparation, 2006) these were
not included for this analysis. Further explanation and
examination of the StoneHinge algorithm may be found
in Keating et al. (StoneHinge: A Hinge Prediction Algo-
rithm Using Rigidity Theory. Manuscript in preparation,
2006).
Table IPerformance of the Predictors Against the Hinge Atlas Gold Annotation
cTest
positiveTrue
positive sensitivity specificity P-value
StoneHinge 1204 42 0.28 0.91 2.7E-11HingeSeq 771 13 0.09 0.94 0.11TLSMD 455 30 0.20 0.97 4.8E-15hNMa 1279 37 0.24 0.91 8.7E-08hNMb 126 31 0.20 0.99 3.2E-33hNMc 517 26 0.17 0.96 1.7E-10hNMd 1545 49 0.32 0.89 1.1E-11hNMe 235 35 0.23 0.99 2.0e-29FO1 563 8 0.05 0.96 0.32FO1M 292 14 0.09 0.98 6.6E-06FO 272 62 0.41 0.98 9.2E-66
Test positives are predicted hinge locations. hNM1 and FO1 give continuous
(rather than discrete) output, normalized to range from 0 to 1 for each protein.
Therefore for hNM1 and FO1 we took values below .02 and 0.1, respectively, as
test positives. There were a total of 13,259 residues in the HAG, of which
152(13,107) were Gold Standard Positives (Negatives). Therefore for the example
of StoneHinge, sensitivity was calculated as 42/152 5 0.28 and specificity was
(13259 2 1204)/13,107 5 0.91. For the same example, P-value was computed as
the probability of finding 42 or more true positive residues in a set of 1204 resi-
dues selected randomly and without replacement from a set of 13,259, using the
cumulative hypergeometric distribution.
S.C. Flores et al.
304 PROTEINS
TLSMD
The second existing method was recently introduced
(TLSMD version 0.8.1 was used here) to identify seg-
ments of a protein that exhibit concerted vibrational
motion.37 It is based on analysis of the spatial distribu-
tion of atomic displacement parameters within a single,
conventionally-refined protein crystal structure. Each
group so identified is modeled by assigning to it a set of
20 TLS (Translation/Libration/Screw) parameters that
describe its net vibrational displacement.38 The method
is capable of identifying both large and small vibratory
groups, and is largely independent of the resolution of
the X-ray data used to refine the crystal structure. The
validity of TLSMD analysis in the context of crystallo-
graphic refinement can easily be judged by tracking the
standard crystallographic residuals R and Rfree resulting
from refinement of TLSMD-generated models against the
original diffraction data. In many cases multigroup TLS
models are strikingly successful at predicting the observed
diffraction data, and out-perform conventional crystallo-
graphic models during refinement.37,39 It is logical to
conclude that TLSMD correctly identifies actual vibra-
tional modes of the protein within the crystal. We are
interested to test the extent to which these same vibra-
tional modes are also present in solution, and the extent
to which the boundaries between vibratory groups identi-
fied by TLSMD correspond to specific hinge points iden-
tified by other experimental methods.
TLSMD partitions the protein chain into N segments. It
currently has no automated mechanism for distinguishing
segment boundaries that might correspond to inter-do-
main hinges from segments boundaries that might, for
example, define the endpoints of a flexible loop. To the
extent that it assigns an order of importance to these
boundaries, it does so based on their relative contribution
to the observed distribution of atomic displacements in
the crystal structure. Thus TLSMD may identify the boun-
daries of highly flexible, albeit small, regions before it
identifies those of large domains whose vibrational ampli-
tude is highly restricted by the crystal lattice. Therefore
each segment boundary, or breakpoint, may possibly cor-
respond to a hinge. But we faced a difficulty in deciding
how many TLSMD breakpoints to compare against the
hinge points listed in HAG. We have chosen to report all
segment boundaries found for N 5 2,3,4,5. This means
that the hinges resulting from assuming 2,3,4, and 5
domains exist are all reported on an equal footing. We
will delve into the consequences of this in the discussion.
FlexOracle (FO1, FO1M, FO)
The last of the existing algorithms to be discussed, Flex-
Oracle, is based on the definition of structural domains as
independently stable subunits of proteins. This means that
cleaving the protein at the hinge site between domains
should result in fragments that maintain their overall
structure,40 because those fragments should have a lower
free energy of folding than fragments generated by cleav-
ing within domains. The algorithm therefore works by
estimating the free energy of folding for all possible pairs
of fragments generated by cutting at two points on the
protein chain, and looking for minima of this quantity.20
FlexOracle has powerful discriminating ability. Sepa-
rate work describes three variants of FlexOracle.20 These
include the single-cut FlexOracle predictor with the
FoldX force field, which we here call FO1, a second pre-
dictor which detects the local minima of the same, which
we call FO1M, and the two-cut FlexOracle predictor,
which here we simply call FO. FO is by far the most
accurate of these as we will show.
Because it cuts the backbone at two points, however, FO
is limited to proteins with single- or double-stranded
hinges. Also, the code neglects bound metals. Since these
are highly coordinated, we will argue that accuracy may be
limited when metal binding contributes significantly to the
stability and motion characteristics of the protein.
Definition of HingeMaster
As pointed out previously, the described algorithms use
substantially different information to make hinge predic-
tions. Consequently they have different strengths and yield
very different results. StoneHinge is good at finding the
general region of the hinge, but often overestimates the
size of the hinge region. hNMd faces similar limitations.
FO and hNMb are very precise but are limited to single
or double-stranded hinges. TLSMD, on the other hand,
makes a small number of predictions, well spaced apart,
one or more of which often lie exactly on or very close to
domain hinges, and the rest of which are incorrect or lie
on points of non-domain hinge flexibility.
Combining various predictors by consensus41 or other
means is not unprecedented. We did this by creating
HingeMaster, the output of which is a weighted vote of
the individual predictors:
xHingeMaster ðiÞ ¼X8c2C
kcxc ðiÞ ð5Þ
where
C ¼ fStoneHinge; FO1; FO1M ; FO; HingeSeq; TLSMD;
hNMa; hNMb; hNMc; hNMd; 1gxcðiÞ ¼ output of predictor c for residue i:
kc ¼ weighting coefficient of predictor c; determined below:
Parameterization of HingeMaster usingLeast Squares Fitting
Least Squares Fitting is a simple method used to pro-
ject vectors onto a certain basis set, much as is done in a
HingeMaster
PROTEINS 305
Fourier Transform to project arbitrary functions into the
basis of harmonic functions. We used the former tech-
nique to find the kc’s in Eq. (5) corresponding to an
optimal predictor. The procedure follows.
Let y 5 a column vector, the components y(i) of
which are the hinge annotations of the m residues in the
HAG, in the format 1 5 hinge, 0 5 nonhinge. The index
i counts over all residues in all proteins of the set in
question, which in this work will be either the training,
test, or complete HAG set. Order is unimportant as long
as the i’s in y are in the same order as the i’s in x, below.
Let x 5 an m 311 matrix, the rows of which will be
used to predict the rows of y. Each column of x is a an
m-component vector xc, such that c [ C. Each compo-
nent xc(i) of each such column vector is the output of
the predictor c for residue i. Correspondingly, x(i)
(without a subscript) is a row vector with 11 components
corresponding to the output each of the 11 predictors
emitted for residue i. Note that the last ‘‘predictor’’ is a
constant term used as an offset.
Let k 5 a column vector, the components kc of whichwill give us the weight to be applied to the various pre-
dictors in order to make the composite HingeMaster pre-
dictor. Thus according to our definition of HingeMaster
[Eq. (5)]:
xLeast�squares ¼ xk � y: ð6Þ
To obtain k, we minimized the quantity (xk 2 y)2.
The least squares regression methodology is a standard
one42 which will not be derived here. The result is that
analytically:
k ¼ ðxTxÞ�1xTy ð7Þ
The above Eq. (7) can be said to train k based on pre-
dictor output and gold standard annotation over some
set of residues i. The best available value of k is likely to
be one fitted using the set of all residues in all proteins
in the HAG, which we designate as {HAG}. That is to
say, in Eq. (7) we use x,y(i | i [ {HAG}) and obtain a
particular value of k which we call kHAG.
Parameterization of HingeMasterusing Boosting
Though simple, Least Squares Fitting results in a
powerful predictor, as will be shown. We nonetheless also
tried fitting the kc’s defined above using an alternate
machine learning technique called Boosting. This is a
standard technique described in,43 which we will briefly
outline here. As for Least Squares Fitting, the goal of
Boosting is to create a stronger classifier based on a series
of predictors with individually weaker performance. In
this setting, the outcomes of the hinge predictors are
used as feature vectors of our learning algorithm, but
instead of analytically minimizing (xk 2 y)2 as before,
we iteratively minimize a loss function e(xk,y) which
decreases exponentially with classification accuracy.
Boosting is a generic technique with several variants,
such as discrete AdaBoost which uses discrete predicted
labels at each iteration of the algorithm. Real AdaBoost
uses class probability estimates rather than discrete labels
to improve accuracy. Other variants change the loss func-
tion to be Logistic and the gradient search method to be
stochastic. For HingeMaster we use an extension of Real
AdaBoost called Gentle AdaBoost.44 It offers the advant-
age of using real valued class labels at each stage plus an
improved numerical performance compared to Real Ada-
Boost.45 The hinge residues comprise a small portion of
total residues, resulting in an imbalanced dataset. Under
these circumstances accuracy can trivially be maximized
by a predictor which classifies all residues as nonhinges.
To deal with this, we modify the method by oversampling
the gold standard hinge residues 99-fold, with re-
placement.46 Gentle AdaBoost is then run for 30 iterations
after which e(xk,y) converges to a minimum value. In the
cross-validation that follows, we use the class probability
estimates as a continuous predictor xprob_Boosting.
Cross-validating Least-SquaresHingeMaster parameters
Clearly HingeMaster, whether trained using Least
Squares Fitting or Boosting, cannot be tested on the
same dataset used to train it. For both cases, we therefore
validate HingeMaster by first randomly separating the 20
homologous pairs of proteins in HAG into a training set
consisting of 15 of these pairs (30 total protein struc-
tures) and a test set consisting of the remaining 5 pairs
(10 protein structures). The set of all residues in all pro-
teins in the training set we call {TRAINING}, while the
set of residues in the test set we call {TEST}. We used
Eq. (7) with the training set data x,y(i | i [ {TRAINING})
to obtain k*, the cross-validation value of k. We then
used this vector with the individual predictor results for
residues in the test set to obtain cross-validated Hinge-
Master results x*HingeMaster(i | i [ {TEST}) as follows:
x�HingeMasterði j i 2 TESTf gÞ ¼ k� � xði j i 2 TESTf gÞð8Þ
We then generated a ROC curve by gradually decreas-
ing the threshold above which values of x*HingeMaster(i | i [{TEST}) were taken to correspond to predicted hinge
locations, and comparing these to the annotated hinge
locations y(i | i [ {TEST}). For each value of the thresh-
old, residues i with scores x*HingeMaster(i) above that
threshold are taken to be test positives. We further classify
the test positives using a strict criterion, meaning that
S.C. Flores et al.
306 PROTEINS
those that coincide exactly with annotated hinges (y(i) 51) are taken as true positives, those that coincide with
nonhinge residues (y(i) 5 0) are taken as false positives,
even if they are immediately adjacent to a hinge residue.
The generation of the ROC curve is explained in more
detail in prior work.20
We repeated the above process a total of 20 times.
Each time, we generated new {TEST} and {TRAINING}
sets by randomly dividing HAG as described. We
obtained 20 different values of k* vectors and generated
20 different sets of HingeMaster predictions. These were
then used to generate ROC curves representing average
performance. We report the average and standard devia-
tion of the HingeMaster parameters k* for Least Squares
Fitting, where these values have an intuitive interpreta-
tion.
We also asked the question, what would happen if we
modified our gold standard hinge definition to include
five residues to the left and right of the HAG hinges?
This is similar to the loose criterion, defined in the
Statistical benchmarks section. Doing this would increase
the number of True Positives at a given HingeMaster
threshold, but would also annotate as ‘‘hinges’’ residues
which clearly belong to a rigid domain. To answer this
question, ROC curves were generated using the thus-wid-
ened HAG definition.
Cross-validating BoostingHingeMaster parameters
We underwent the process described above, with
minor variations, to cross-validate the Boosting parame-
ters. Instead of xleast2squares, we of course used xBoosting.
The {TEST} and {TRAINING} sets were generated in pre-
cisely the same way, but iteratively minimizing e(xk, y)rather than (xk2y)2 resulted in different values of k*even for the same data. The sum in Eq. (5) was con-
verted into a class probability xprob_Boosting as mentioned.
In every other respect the ROC curves were generated
precisely as above, by varying the threshold value of
xprob_Boosting above which a residue was taken to be a
hinge.
RESULTS
Weighting and evaluation of predictors
The fitting of kHAG and k* was carried out as
described above. The averages and standard deviations of
the resulting weighting factors are shown in Table II. We
evaluate the predictors using the statistical measures of
sensitivity (true positives/gold standard positives), speci-
ficity (true negatives/gold standard negatives), and
P-value (see discussion) in Table I. Note that these were
computed under the strict criterion, meaning that a test
positive was considered to be a false positive if it coin-
cided with a nonhinge residue, even if it was immediately
adjacent to an annotated hinge residue. The statistical
measures are explained in detail in the Supplementary
methods section and in prior work.20 The average ROC
curves generated from the HingeMaster 20-fold cross-val-
idation are shown in Figure 3. Four curves are shown,
representing the two methods (Least Squares and Boost-
ing), each trained and tested with two different gold
standards (unmodified and widened HAG).
Table IIFitting of kc
HAG and kc*
c
xc
kcHAG
kc*
Description of cPredictedhinge
Predictednon-hinge Average
Standarddeviation
1 1 1 0.042 0.062 0.010 Dummy constant for fittingN 1 0 0.012 0.012 0.003 StoneHinge flexible regionsHingeSeq high low 0.004 0.004 0.001 Raw HingeSeq score; high values more likely hinge locationsTLSMD 0 1 20.029 20.048 0.009 TLS domain boundary, for N 5 2.5 putative domainshNM1 low high 20.010 20.010 0.003 First normal mode displacementhNMb 1 0 0.190 0.196 0.030 Continuous Domain Boundary Identifier most likely hinge locationhNMc 2,3,4.. 0 0.028 0.035 0.007 Secondary hinge predictions similar to but not reported by
the Continuous Domain Boundary IdentifierhNMd 1 0 20.0007 20.0006 0.0007 Regions excluded from contiguous domainsFO1 low high 20.008 20.012 0.002 Single-cut FlexOracle (with FoldX) energy, normalized
from 0 to 1. <0.05 5 hingeFO1M 1 0 0.014 0.015 0.008 Minima of single-cut FlexOracle energy, identified
per Flores et al.FO 1 0 0.189 0.165 0.022 Two-cut FlexOracle prediction
Values of c are given in the left column. The output xc is given for predicted hinge and predicted nonhinge residues, for each predictor c. For example, hNMa gives out-
put ranging continuously from 0 to 1, with the lower values more likely to correspond to hinge locations. hNMb, on the other hand, gives discrete output: 1 for pre-
dicted hinge locations and 0 for predicted non-hinge locations. Note that the sign of kc corresponds to whether higher or lower values correspond to hinges for that
predictor. c 5 1 is a dummy constant which compensates for the difference in mean values of predictors x vs. gold standard annotation y.
HingeMaster
PROTEINS 307
Although the above summarizes the results of the vari-
ous predictors, it is illustrative to review the results of
the various predictors individually, for the 40 proteins in
the HAG. We made an online gallery of results for that
purpose at http://molmovdb.org/HAG. Links in this table
for each protein in HAG lead to a morph page showing
the motion between open and closed form of the protein,
results of running the various predictors on the open
and closed conformation, and the Protein Data Bank
(PDB) information page for the associated PDB-depos-
ited structure files. We also chose two of the forty pro-
teins to discuss in detail here (Figs. 2 and 4 and below),
and six more in the supplementary information.
Glutamine binding protein (GlnBP) (open)
Morph ID: f927198-20246 PDB ID: 1GGG
HAG hinges (residues 89,90,178–182)
Examination of results for individual proteins can
bring out salient features of the various predictors. As a
first example, we present Glutamine binding protein
(GlnBP). GlnBP of E. coli resides in the periplasmic
space, where it binds L-glutamine and subsequently
undergoes a conformational change that allows it to be
recognized by the membrane-bound components of the
permease system, which subsequently translocate the
nutrient into the cytoplasm against a concentration
gradient.
GlnBP is comprised of two domains linked by a hinge
region, the approximate location of which was arrived
upon by various authors using different methods. Pang
et al. annotated the hinge location by taking two extreme
projections of the protein coordinates along the second
normal mode eigenvector, and then used Hingefind to
identify a hinge point at residues 88 and 183, based on
these two structures.47 This is very different from the
HAG annotation procedure, which used two different
crystallographically obtained conformations of the pro-
tein. The so-named large domain contains both the N-
and C-termini and consists of two stretches of polypep-
tide, residues 1–84 and 186–226 according to Hsiao
et al.48 The small domain therefore consists of a single
stretch of polypeptide from residues 90–180. Hsiao et al.
simply took the entire PROCHECK49-identified antipar-
allel b-stranded region connecting the two domains (resi-
dues 85–89 and 181–185), as a hinge, again referring to
only one structure.
hNMb, and hNMd [Fig. 2(a,b) and 5(c)], and FO
[Fig. 2(c) and 5(c)], were successful, but hNMd overpre-
dicted the extent of the hinge region. Stonehinge frag-
mented the largest domain into several smaller domains
[Fig. 5(c)]. Thus, its predictions correspond to a flexible
loop in the second domain. The StoneHinge output
noted that this prediction likely did not correspond to
domain motion; however, as explained above, this note
was ignored for the HingeMaster predictions.
The TLSMD partition into 3 chain segments for
1GGG:A (Chain A) is quite accurate, placing the segment
boundaries at 88/89 and 182/183 [Fig. 5(c)]. For the sec-
ond chain in the structure, 1GGG:B, TLSMD instead
finds a boundary at 168/169 in the 3-segment split. The
TLSMD analyses of both chains A and B agree on N 5 4
boundaries at residues 90 � 2, 169 � 1, and 190 � 1.
The false positive boundary at 44/45 seen in this figure is
introduced when a 5th chain segment is requested.
hNMa shows global minima near the HAG hinges,
while FO1 is less clear about this. HingeMaster (with
Least Squares fitting) displays very clear peaks at or very
near the HAG hinges [Fig. 2(e)]. The ‘‘color by Hinge-
Master flexibility’’ feature available on our server is illus-
trated in Figure 2(d), where strong hinge predictions can
be seen to lie on the linker connecting the two domains.
Human lactoferrin
Morph ID: f964647-15593 PDB ID: 1LFG
HAG hinges: 90,91,250,251
Human lactoferrin (hLF) is an iron-binding glycopro-
tein found in exocrine fluids produced by mammals,
including milk, saliva, tears, bile, pancreatic fluid, and
mucous secretions. It has broad spectrum antibacterial
Figure 3ROC curves representing average performance of HingeMaster in 20-fold cross-
validation tests. Least Squares (thick continuous red line) had slightly greater
Area Under the Curve (AUC) than Boosting (thick dashed black line), but the
slope at the origin was slightly greater for Boosting. When instead of the HAG
we used a gold standard which included five residues on each side of every HAG
hinge (similar to our loose criterion), performance deteriorated (thin continuous
red and thin dashed black lines represent Least Squares and Boosting,
respectively).
S.C. Flores et al.
308 PROTEINS
Figure 4Human lactoferrin (open, apo form), Morph ID: f964647-15593 PDB ID: 1LFG, HAG hinges: 90,91,250,251. In (a), the HAG hinge is shown in green, with domains on
either side colored differently. As seen in (b), HingeMaster makes a strong prediction for a hinge at residue 332 (four algorithms in agreement, C, see Figure 2 caption for
legend). This location does not appear in the HAG, but a search of the literature uncovered evidence for a hinge here. Lactoferrin is organized into two homologous
halves, named the N and C lobes. Each of these lobes is further subdivided into two domains: N1 and N2 in the N lobe and C1 and C2 in the C lobe. The opening of
these domains exposes an iron binding site in each lobe.52 The motion selected for Hinge Atlas Gold shows the N1 domain (shown in blue) rotating relative to the rest of
the molecule exposing the binding site in the N-lobe. Thus, the HAG hinges are located between the N1 and N2 domains. The hinge most strongly predicted by
HingeMaster, however, falls in between the C1 and N2 lobes and contributes to the movement of the two lobes relative to each other. As in the case of Troponin C,
experimental evidence is found for this hinge, as lactoferrin crystals grown at 277 and 303 K show rotation between the two lobes (Karthikeyan et al.). None of the
predictive measures identify a hinge point at 90/91 in the open form structure. However TLSMD analysis of the closed form of the same protein (PDB entry 1LFH;
Morph ID f964705-18231) finds segment boundaries at 91/92 and 249/250 for the 3-segment partition, corresponding exactly to the lactoferrin mobile domain boundaries
(not shown).
HingeMaster
PROTEINS 309
Figure 5Predictor results for HAG proteins at a glance (panels a-d). Rule at top indicates residue number along protein chain. Each protein is marked with protein name. Light
blue track represents residue numbers spanned by each protein. Green boxes indicate location of HAG hinge. Cyan, magenta, red, orange, blue, and purple bars indicate
hinge location predicted by FO, FO1M, StoneHinge, TLSMD, hNMb, and hNMd, respectively.
S.C. Flores et al.
310 PROTEINS
Figure 5(Continued)
HingeMaster
PROTEINS 311
Figure 5(Continued)
S.C. Flores et al.
312 PROTEINS
Figure 5(Continued)
HingeMaster
PROTEINS 313
properties and seems to regulate the absorption and
excretion of iron in infants.50
The hinge bending motion of lactoferrin has been
studied in detail. The protein consists of N- and C-termi-
nal lobes which are highly homologous and are presumed
to have arisen from gene duplication. Each lobe is further
subdivided into two domains, N1 and N2, and C1 and
C2. In the iron-free form, a deep cleft appears between
N1 and N2. No such cleft appears in the C-lobe either in
the iron free or iron bound form, but this is believed to
be an artifact of crystallization. In the iron-bound form,
N1 and N2 are close together about a common hinge,
located between residues 90 and 91, and 250, and 251
according to Gerstein et al.51 This is in perfect agree-
ment with the independent annotation made in this
work.
The results for this protein are shown in Figure 4.
HingeMaster makes a strong prediction for a hinge at
residue 332 (StoneHinge TLSMD, hNMb, and hNMd in
agreement). This chain location does not appear in the
HAG, but a search of the literature uncovered evidence
for a hinge at this location. Lactoferrin is organized into
two homologous halves, named the N and C lobes. Each
of these lobes is further subdivided into two domains:
N1 and N2 in the N lobe and C1 and C2 in the C lobe.
The opening of these domains exposes an iron binding
site in each lobe.52 The motion selected for HAG shows
the N1 domain (in blue) rotating relative to the rest of
the molecule exposing the binding site in the N-lobe.
Thus, the HAG hinges are located between the N1 and
N2 domains. The hinge most strongly predicted by Hinge
Master, however, falls in between the C1 and N2 lobes
and contributes to the movement of the two lobes rela-
tive to each other. As in the case of Troponin C, experi-
mental evidence is found for this hinge, as lactoferrin
crystals grown at 277 and 303 K show rotation between
the two lobes (Karthikeyan et al.).
None of the predictive measures identify a hinge point
at 90/91 in the open form structure. However TLSMD
analysis of the closed form of the same protein (PDB
entry 1LFH; Morph ID f964705-18231) finds segment
boundaries at 91/92 and 249/250 for the 3-segment parti-
tion, corresponding exactly to the lactoferrin mobile
domain boundaries (not shown).
DISCUSSION
After completing the calculations, we carried out our
analysis of the hinge finding algorithms on two levels:
the quantitative level, which consisted of examining vari-
ous statistical benchmarks, and the qualitative level,
which consisted of interpreting results for individual pro-
teins. In this section we will discuss the quantitative sum-
maries and will also point out advantages and disadvan-
tages of the algorithms through the specific examples
presented in here and in the supplementary information.
In this section as before we will focus on StoneHinge,
TLSMD, hNMb, and FO, and to a lesser extent hNMd,
only intermittently referring to the various other subsidi-
ary predictors and HingeSeq.
Statistical benchmarks
We begin to get an idea of the predictive value of the
various methods from the weight assigned to each pre-
dictor, in Table II. Here, we see that hNMb and FO
receive by far the highest weights, hinting at high predic-
tive power, while TLSMD and StoneHinge get a more
moderate weight and hNMd gets almost no weight. This
cannot be taken as a rigorous statistical benchmark, how-
ever, since the predictors are not independent, and some,
such as FO and FO1M, are in fact very closely related.
For greater rigor, we computed the sensitivity, specificity,
and P-value associated with each predictor in Table I.
These statistical measures are explained in detail in prior
work.20
The sensitivity (true positives/gold standard positives)
was highest for FO, followed by Stonehinge, TLSMD, and
hNMb. FO was thus able to find the largest number of
hinge residues (62). As is customary we also report the
specificity (true negatives/gold standard negatives).
hNMb had the highest specificity, followed closely by FO
and TLSMD. Stonehinge and hNMd have lower specific-
ity, reflecting a tendency to predict the correct hinge
location but also to report a wide region about the anno-
tated hinge location as a predicted hinge. We also eval-
uated the statistical significance by postulating a null
hypothesis that the test positive residues were taken ran-
domly and without replacement from the population of
residues in HAG. Under this hypothesis, the mean fre-
quency of hinges is the same in the test positive set as in
HAG. For each predictor, we computed the probability of
finding the observed number or more of annotated hinge
residues in a randomly selected set equal in size to the
number of test positives reported by the predictor. We
computed this quantity using the cumulative hypergeo-
metric distribution.20 Clearly, FO has the highest statisti-
cal significance (lowest probability that the null hypothe-
sis is correct). hNMb has a higher (but still impressive)
P-value than FO.
Part of the reason FO had lower specificity than
hNMb is because FO only attempts cuts on the backbone
at four residue intervals, while hNMb probes every possi-
ble pair of residues as a possible continuous domain
boundary. As a result, FO predicts four-residue wide
windows as possible hinge locations, with some uncer-
tainty as to the exact location of the best putative hinge.
hNMb, on the other hand, reports two-residue windows
as putative hinge locations, and these are presumed to be
the best choice of hinge possible for that method.
S.C. Flores et al.
314 PROTEINS
With regard to the P-value, the reader should recall
that this quantity changes based on the size of the data-
set. Therefore this number can only be used to compare
predictors tested on the same data. By this measure, FO
was by far the most discriminating predictor, followed by
hNMb.
As explained earlier, the sensitivity, specificity, and
P-value were computed under the strict criterion for sta-
tistical rigor. However, for an application most users
would probably consider a prediction that came within
about five residues of the correct hinge location to be a
true positive. So we examined each of the 40 proteins
and labeled each as a success, partial success, or failure
on the basis of a loose criterion for each predictor c. A
test was considered a success under this criterion if each
prediction came within five residues of an annotated
HAG hinge, and vice versa. It was a partial success if at
least one prediction matched one HAG hinge, but one or
more predictions were more than five residues from a
HAG hinge, or vice versa. It was a failure if no predic-
tions were within five residues of a HAG hinge. The eval-
uation for each protein under the loose criterion is pre-
sented in supplementary Table V.
We counted the number of successes, partial successes,
and failures for the five most interesting predictors in Ta-
ble III. As can be seen, FO scored the most successes, fol-
lowed by hNMd and hNMb. TLSMD had no successes,
but this is due to the fact that as implemented on our
server it reports all domain boundaries for up to five
domains. Since the proteins in HAG have at most three
hinges, some of the TLSMD predictions would be
expected to have no corresponding HAG hinge.
FlexOracle (FO)
The FlexOracle algorithm has the best predictive ability
by several measures. It had the highest sensitivity and
lowest P-value (Table I). It had the most successes under
the loose criterion (Table III). Results for individual pro-
teins (supplementary Table V) show that FO failed for
Calmodulin, Troponin C, and Elastase of Pseudomonas
Aeruginosa, suggesting the method cannot deal well with
proteins that depend on bound metals for stability and
motion. It also fared poorly for the two proteins with
three hinge points, as would be expected for a predictor
intrinsically limited to two hinge points (supplementary
Table V).
hNMb, hNMd
hNMb and hNMd are complemented by FO, as can be
seen by several cases for which FO fails but hNMb and/
or hNMd succeed (Fig. 5), as was the case for five pro-
teins: the (open) metal-bound form of calmodulin, bac-
teriophage T4 lysozyme (closed), cAMP dependent pro-
tein kinase (closed), elastase of pseudomonas aeruginosa
(open), and inorganic pyrophosphatase (closed).
The hNMd method has a strong advantage in that
unlike FO and hNMb, it is not intrinsically limited by
the number of strands in the hinge. In particular, we
note that FO and hNMb both completely failed to pre-
dict the triple stranded hinge in cAMP dependent protein
kinase, while Stonehinge and TLSMD either failed or had
partial success. For the closed form of this protein hNMd
was the only successful predictor. For the open form, one
of the three hinge points is in a disordered region that
does not appear in the crystal structure. hNMd has a
cluster of hinge predictions centered about that break in
the chain and therefore it was arguably as successful as
could be expected under the circumstances. The same
argument could not be made for the other predictors, as
the reader can verify by examining Figure 5.
In general, we find that residues identified by hNMd
coincide to a high degree with the general location of the
hinge. However the predicted hinge regions were broad,
lowering the specificity and raising the P-value.
TLSMD
As mentioned earlier, because hinges for N 5 1,2,3,4,5
are reported together, the set of TLSMD ‘‘hinge predic-
tions’’ for each protein will be larger than the actual
number of hinge points. That is, the forced partition of a
3-domain protein into only two segments will tend to
create a ‘‘false’’ breakpoint somewhere inside the middle
domain, rather than finding either of the two ‘‘true’’ do-
main boundaries. Even if the two correct boundaries are
found by the TLSMD partitions for N � 3, this initial
false prediction will remain in the prediction set. This
results in a poorer showing on a ROC curve if the extra
predictions are treated as false positives. An alternative
would have been to manually filter out these extra break-
points based on visual inspection of the structure, but we
were reluctant to introduce possible experimentor bias.
On the basis of the outcome of the evaluations presented
here, and on the observed distribution of actual hinge
points in the larger set of TLSMD breakpoints, we hope
to be able to automate such filtering in the future. To a
significant extent, however, this filtering is done by Hin-
geMaster. The StoneHinge, hNMa, hNMd, and FO1 pre-
dictors, which have many predictions and low specificity,
Table IIISummarized Performance Under the Loose Criterion
StoneHinge TLSMD hNMb hNMd FO
Successes 8 0 17 19 23Failures 20 12 14 13 12Partial successes 12 28 9 8 5
HingeMaster
PROTEINS 315
tend to ‘‘select’’ the TLSMD breakpoints corresponding
to domain hinge motion, while ‘‘deselecting’’ those corre-
sponding to fragment hinges or other motions.
We found that some of the hinges predicted by
TLSMD were close to HAG hinges with high frequency.
The remaining TLSMD predictions often correctly
reflected motions of fragments smaller than domains,
and these tended not to coincide with the predictions of
other methods. An additional stage of either manual or
automated curation of the TLSMD results would remove
most of these fairly easily. In particular, TLSMD would
benefit greatly from an improved ability to combine mul-
tiple chain segments from the initial analysis to yield a
description of ‘domains’ in the usual sense. The MurA
analysis in the supplements provides a good example of
this. The essential features of the structure are captured
well by the TLSMD partition into six continuous chain
segments. The close three-dimensional proximity of the
boundaries at residues 20/21 and 228/229 are easily inter-
preted as belonging to a single inter-domain hinge; the
further subdivision of the obvious continuous domain
into three chain segments is easily interpreted as the
presence of a small flexible loop (residues 108–127) pro-
truding from a larger continuous domain. The C-termi-
nal tail of 20 residues is also flexible, but is not relevant
to the primary inter-domain flexibility. Thus a curated
interpretation of the TLSMD analysis of MurA would list
three features: A two domain protein with an inter-do-
main hinge points at residues 20/21 and 228/229; a sec-
ondary set of hinge points corresponding to a flexible-
loop (108–127) in one of the domains; and a flexible C-
terminus.
StoneHinge
We discussed the fact that TLSMD overpredicts, since
it reports more hinges than are annotated in HAG.
StoneHinge also had a significant rate of false-positive
hinge predictions (Table IV), This is typically caused by
StoneHinge underpredicting the size of the rigid
domains, such as in the open form of ovotransferrin. In
that case, StoneHinge predicted that the second domain
spanned residues 121–171. However, observation of the
motion reveals that this domain spans residues 93–245.
This underprediction of the rigid domain leads Stone-
Hinge to overpredict the span of the hinge. Additionally,
a number of StoneHinge’s over- and mis-predictions are
flagged as such by StoneHinge. As noted above, if either
rigid domain is predicted to be less than twenty residues,
StoneHinge reports that the predicted hinges are unlikely
to correspond to domain motion (again, this eventuality
is ignored for HingeMaster).
We note that when both TLSMD and StoneHinge pre-
dict a hinge, two-thirds of the time it coincides with a
HAG hinge. Likewise, most experimentally defined hinges
are predicted by either StoneHinge or TLSMD, account-
ing for the substantial weight they receive in HingeMas-
ter. In the cases where either StoneHinge or TLSMD
misses a hinge, it is usually predicted by at least one of
the other predictors. Notably, experimentally defined
hinges virtually always occur within the lower 10% of the
hNMa atomic displacement function. Accordingly, the
predictive confidence of HingeMaster is strong when at
least three of these methods predict a hinge at a given
site (or within a few residues of it). As with computa-
tional hinge detection, experimentally defined hinges can
be identified based on different criteria. For instance, one
researcher might identify them based on the observation
of large, localized, noncompensatory changes in main-
chain dihedral angles, whereas another might identify
hinges based on large main-chain B-values (which can
reflect rigid-body motions of a well-ordered structure in
one case, but a lack of well-defined local structure in
another). Thus, there is a distinct possibility that the var-
ious hinge predictors are identifying hinges that represent
different mechanisms of motion, especially with regard to
how localized or disseminated that motion is. By defining
different hinge mechanisms and algorithms for detecting
them, we hope to ultimately clarify the kinds of motion
that occur in proteins, and provide tools that will aid in
annotating experimental structures.
Least squares versus Boosting,and width of hinge region
The Least Squares method of training HingeMaster
resulted in a powerful predictor, as demonstrated by a
ROC curve with large Area Under the Curve (AUC) and
high, nearly vertical slope at the origin. We nonetheless
investigated whether a more sophisticated algorithm
could improve results. Despite its additionally complexity
Boosting was found to yield results only marginally dif-
ferent from those of Least Squares fitting (see Fig. 3).
One must bear in mind that the hinge residues are a
small portion of total residues, therefore the Gold Stand-
ard Positives used for training are a very small set. Under
these circumstances, classifiers with many adjustable pa-
rameters suffer from the problem of overfitting,53 and
Table IVPredictors at a Glance
Predictor Basis Max. hinge points
FlexOracle Free Energy of folding 2hNMb Normal modes 2hNMd Normal modes No limitTLSMD Experimental thermal factors No limitStoneHinge Bond network topology No limit
Three of the predictors have no limit on number of hinge points in principle but
on our server TLSMD only reports boundaries based fragmenting the protein into
as many as to 5 domains. Domain motions with a very large number of hinges
are unlikely for proteins of the size range considered here.
S.C. Flores et al.
316 PROTEINS
simpler methods are appropriate. The version of Hinge-
Master offered on our server and discussed in most of
this work was trained using the Least Squares method.
We also sought to determine whether HingeMaster
would benefit from training with a gold standard that
included not only the HAG hinges, but in addition all
residues within five residues of the nearest HAG hinge,
similar to the loose criterion. This is a much more for-
giving definition of the hinge. However the gold standard
thus generated included residues which clearly belonged
to one or another rigid domain and so was of lower
quality. Correspondingly, the results were found to dete-
riorate for Least Squares as well as Boosting, as evidenced
by ROC curves with significantly lower AUC (Fig. 3).
Complementarity of methods
Since the various predictors are based on very different
information (Table IV), their strengths and weaknesses
are complementary. In particular, FO and hNMb are lim-
ited to single- and double-stranded hinges. hNMd, how-
ever, has no such limitation and may be more successful
in these cases (supplementary Table V). Similarly, FO is
susceptible to bound metals that play a significant role in
stabilizing the protein, but hNMb and hNMd is reason-
ably successful in these cases. TLSMD is comparatively
weak at distinguishing domain from non-domain
motion, but can find smaller scale motions not detected
by FO and hNMb, and its accuracy is unaffected by
bound metals. Stonehinge lacks precision but is good at
finding the general region of the hinge. Altogether, only
a few hinges escaped detection by one or another of the
methods. The combination of highly specific predictors
which usually did well but were sometimes somewhat off
the mark, with predictors which identified broad swathes
where the hinges were likely to be, resulted in a predictor
of variable sensitivity, as we will discuss. The output of
HingeMaster strongly indicates the pinpointed location
of the hinge predicted by FO and hNMb, but less dra-
matically points out alternative locations. When inter-
preted by a critical eye, these results could bring insight
even when one or more of the predictors are incorrect.
Some of this is visible in the results for individual pro-
teins as discussed.
CONCLUSIONS
We demonstrated the strengths and weaknesses of sev-
eral predictors, including a set of normal mode based
tools. We show that for 29 of the 40 proteins in HAG at
least one predictor is completely successful under the
loose criterion. For 10 of the remaining 11, at least one
predictor was partly successful. HingeMaster weighs the
correlation of each predictor to the HAG hinge annota-
tions and presents the combined results in a visually
understandable way. This combined predictor is shown
to robustly produce ROC curves demonstrating high pre-
dictive power.
WEB TOOLS
Hinge prediction server
Most of the predictors discussed here can be run by
the public on single-chain proteins by making a submis-
sion through the hinge prediction server linked from the
front page of our server, molmovdb.org. When the job is
complete, the user receives an email with a link to the
generated morph page. The ‘‘Hinge Analysis Tools’’ box
has links to output from the five predictors. The most
useful of these is the ‘‘Combined predictor page,’’ which
shows the results of all analyses in a single graph, as was
done for this article. Also, buttons are available to high-
light the hinges predicted by HingeMaster, TLSMD, and
StoneHinge in the jmol window. It is possible to color
the protein by HingeMaster flexibility, as we will describe
below.
Hinge annotation tool
To manually annotate the hinges in a submitted pro-
tein, one can use the Hinge Annotation Tool in the hinge
analysis toolbox, on the morph page. This tool consists
of three rows of arrow buttons which allow for the selec-
tion of up to three hinge locations. A ‘‘?’’ button on each
row returns the residue number of the current selec-
ted hinge location. A ‘‘Show all’’ button highlights all
selected hinge locations. A ‘‘Reset highlighting’’ button
returns to the default view. The ‘‘Submit’’ button must
be clicked for these annotations to be entered into our
database. There will appear a ‘‘display public hinge’’ but-
ton which will allow all users to view the selected resi-
dues in the jmol window. With minor modification, this
tool was used to annotate the HAG hinge locations used
in this work. It is possible to create rendered images with
hinges highlighted as we explain below.
Render studio
As discussed above, high resolution ‘‘domain style’’
images similar to those in the figures can be generated
by the public by following these steps:
1. Select up to three hinge points using the Hinge Anno-
tation Tool, as described above. Click on the ‘‘Submit’’
button.
2. Orient the molecule to the desired perspective by
clicking and dragging in the Jmol window.
3. Click on the ‘‘color by domain’’ link.
The coloration of the domains goes by the following
logic. All the residues prior to the first hinge point are
HingeMaster
PROTEINS 317
assigned to domain D1, all the residues between the first
and second hinge points belong to D3, all the residues
between the second and third hinge points belong to D1,
and all subsequent residues belong to D3, and so on. The
hinge residues themselves belong to D2. D1 is colored or-
ange, D2 is green, and D3 is blue.
To color by HingeMaster flexibility step 1 above is
unnecessary; in step 3 click instead ‘‘color by HingeMaster
score.’’ In either case after a slight delay, a pop-up window
will display the generated image. A variant of this tool was
used to generate some of the images in this paper.
ACKNOWLEDGMENTS
Authors thank Cheryl Leung for extensive help with
the preparation of this manuscript, Nat Echols for help-
ing with the web server, Mihali Felipe for systems admin-
istration help, and Burak Erman and Xin Chen for illu-
minating mathematical discussions. Parts of this work
were discussed and refined at the workshop ‘‘Dynamics
under Constraints’’ at Bellairs Research Institute of
McGill University, Holetown, Barbados, January 2006.
REFERENCES
1. Gerstein M, Jansen R, Johnson T, Tsai J, Krebs W. Studying Macro-
molecular Motions in a Database Framework: from Structure to
Sequence. Rigidity Theory Appl 1999:401–442.
2. Krebs W. The database of macromolecular motions: a standardized
system for analyzing and visualizing macromolecular motions in a
database framework. Dissertation. New Haven: Yale University.
3. Shatsky M, Nussinov R, Wolfson HJ. Flexible protein alignment
and hinge detection. Proteins 2002;48:242–256.
4. Janin J, Wodak SJ. Structural domains in proteins and their role in
the dynamics of protein function. Prog Biophys Mol Biol 1983;
42:21–78.
5. Thorpe MF, Jacobs DJ, Chubynsky MV, Phillips JC. Self-organiza-
tion in network glasses. J Non-Cryst Solids 2000;266–269:859–866.
6. Jacobs DJ, Rader A, Kuhn LA, Thorpe MF. Protein flexibility pre-
dictions using graph theory. Proteins 2001;44:150–165.
7. Thorpe MF, et al. Protein flexibility and dynamics using constraint
theory. J Mol Graph Model 2001;19:60–69.
8. Hespenheide BM, et al. Identifying protein folding cores from the
evolution of flexible regions during unfolding. J Mol Graph Model
2002;21:195–207.
9. Rader AJ, et al. Protein unfolding: rigidity lost. Proc Natl Acad Sci
USA 2002;99:3540–3545.
10. Wells S, et al. Constrained geometric simulation of diffusive motion
in proteins. Phys Biol 2005;24:S127– S136.
11. Flores S, et al. The database of macromolecular motions: new fea-
tures added at the decade mark. Nucleic Acids Res 2006;34 (Data-
base issue):D296–D301.
12. Bahar I, Atilgan AR, Erman B. Direct evaluation of thermal fluctua-
tions in proteins using a single-parameter harmonic potential. Fold
Des 1997;2:173–181.
13. Kundu S, Sorensen DC, Phillips GN, Jr. Automatic domain decom-
position of proteins by a Gaussian Network Model. Proteins 2004;
57:725–733.
14. Dumontier M, et al. Armadillo: domain boundary prediction by
amino acid composition. J Mol Biol 2005;350:1061–1073.
15. Flores S, et al. Hinge Atlas: relating sequence features to sites of
structural flexibility. BMC Bioinformatics 2007:167.
16. Nagarajan N, Yona G. Automatic prediction of protein domains
from sequence information using a hybrid learning system. Bioin-
formatics 2004;20:1335–1360.
17. Marsden RL, McGuffin LJ, Jones DT. Rapid protein domain assign-
ment from amino acid sequence using predicted secondary struc-
ture. Protein Sci 2002;11:2814–2824.
18. Schlessinger A, Rost B. Protein flexibility and rigidity predicted
from sequence. Proteins 2005;61:115–126.
19. Painter J, Merritt EA. A molecular viewer for the analysis of TLS
rigid-body motion in macromolecules. Acta Crystallogr D Biol
Crystallogr 2005;61 (Part 4):465–471.
20. Flores S, Gerstein M. FlexOracle: predicting hinges by identification
of stable domains. BMC Bioinformatics 2007;8:215.
21. Yang LW, Bahar I. Coupling between catalytic site and collective dy-
namics: a requirement for mechanochemical activity of enzymes.
Structure 2005;13:893–904.
22. Nicolay S, Sanejouand YH. Functional modes of proteins are
among the most robust. Phys Rev Lett 2006;96:078104.
23. Alexandrov V, et al. Normal modes for predicting protein motions:
a comprehensive database assessment and associated Web tool.
Protein Sci 2005;14:633–643.
24. Krebs WG, et al. Normal mode analysis of macromolecular motions
in a database framework: developing mode concentration as a use-
ful classifying statistic. Proteins 2002;48:682–695.
25. Chennubhotla C, et al. Elastic network models for understanding
biomolecular machinery: from enzymes to supramolecular assem-
blies. Phys Biol 2005;2:S173–S180.
26. Alexandrov V, Gerstein M. Using 3D Hidden Markov Models that
explicitly represent spatial coordinates to model and compare pro-
tein structures. BMC Bioinformatics 2004;5:2.
27. Yang LW, et al. iGNM: a database of protein functional motions based
on Gaussian NetworkModel. Bioinformatics 2005;21:2978–2987.
28. Tirion MM. Large amplitude elastic motions in proteins from a sin-
gle-parameter, atomic analysis. Phys Rev Lett 1996;77:1905–1908.
29. Haliloglu T, Bahar I, Erman B. Gaussian dynamics of folded pro-
teins. Phys Rev Lett 1997;79:4.
30. Holm L, Sander C. Parser for protein folding units. Proteins 1994;
19:256–268.
31. Maxwell J. On the calculation of the equilibrium and stiffness of
frames. Philos Mag 1864;27:294–299.
32. Tay T-S, whiteley W. Recent advances in generic rigidity of struc-
tures. Struct Topol 1985;9:31–38.
33. Jacobs DJ, Bruce H. An algorithm for two-dimensional rigidity per-
colation: The pebble game. J Comput Phys 1997;137:346–365.
34. Lindahl E, Hess B, van der Spoel D. GROMACS 3.0: A package for
molecular simulation and trajectory analysis. J Mol Model 2001;7:
306–317.
35. Berendsen HJ, van der Spoel D, van Drunen R. GROMACS: A mes-
sage-passing parallel molecular dynamics implementation. Comput
Phys Commun 1995;91:43–56.
36. Gohlke H, Kuhn LA, Case DA. Change in protein flexibility upon
complex formation: analysis of Ras-Raf using molecular dynamics
and a molecular framework approach. Proteins 2004;56:322–37.
37. Painter J, Merritt EA. Optimal description of a protein structure in
terms of multiple groups undergoing TLS motion. Acta Crystallogr
D Biol Crystallogr 2006;62 (Part 4):439–450.
38. Schomaker V, Trueblood KN. On the rigid-body motion of mole-
cules in crystals. Acta Crystallogr B 1968;24:63–76.
39. Winn MD, Isupov MN, Murshudov GN. Use of TLS parameters to
model anisotropic displacements in macromolecular refinement.
Acta Crystallogr D Biol Crystallogr 2001;57 (Part 1):122–133.
40. Sedgwick B, et al. Functional domains and methyl acceptor sites
of the Escherichia coli ada protein. J Biol Chem 1988;263:4430–
4433.
41. Jones S, et al. Domain assignment for protein structures using a
consensus approach: characterization and analysis. Protein Sci 1998;
7:233–242.
S.C. Flores et al.
318 PROTEINS
42. Drapper N, Smith H. Applied regression analysis, 2nd ed. Wiley Se-
ries in Probability and Mathematical Statistics. Chichester, GB:
Wiley; 1981.
43. Schapire R. The boosting approach to machine learning: an over-
view. MSRI Workshop on Nonlinear Estimation and Classification,
2002.
44. Friedman J, Hastie T, Tibshirani R. Additive logistic regression: a
statistical view of boosting. The Annals of Statistics 2000;38:337–
374.
45. Culp M, Johnson K, Michailidis G. ada: an R package for stochastic
boosting. Journal of Statistical Software 2006;17(2).
46. Chawla NV, et al. J Artif Intelligence Res 2002;16:341–378.
47. Pang A, et al. Interdomain dynamics and ligand binding: molecular
dynamics simulations of glutamine binding protein. FEBS Lett 2003;
550:168–174.
48. Hsiao CD, et al. The crystal structure of glutamine-binding protein
from Escherichia coli. J Mol Biol 1996;262:225–242.
49. Laskowski RA, et al. PROCHECK: A program to check the stereo-
chemical quality of protein structures. J Appl Cryst 1993;26:283–291.
50. Davidsson L, et al. Influence of lactoferrin on iron absorption from
human milk in infants. Pediatr Res 1994;35:117–124.
51. Gerstein M, et al. Domain closure in lactoferrin. Two hinges pro-
duce a see-saw motion between alternative close-packed interfaces.
J Mol Biol 1993;234:357–372.
52. Norris GE, Anderson BF, Baker EN. Molecular replacement solution
of the structure of apolactoferrin, a protein displaying large-scale
conformational change. Acta Crystallogr B 1991;47 (Part 6):998–
1004.
53. 2007 10 November 2007 [cited; Available from: http://en.wikipedia.
org/wiki/Overfitting].
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PROTEINS 319